1. Field of the Invention
The present invention relates generally to high-precision frequency standards, or as they are more popularly termed, “atomic clocks”, and more specifically to frequency standards that employ coherent population trapping, or CPT.
2. Description of Related Art
Timekeeping devices work by keeping track of the number of times a phenomenon that has a regular period occurs. With pendulum clocks, the regular phenomenon is the swing of the pendulum; with clocks that run on alternative current (AC), it is the cycles of the AC; with clocks that employ quartz crystals, it is the internal vibrations of the quartz crystal.
The most precise clocks are the so-called atomic clocks. In these clocks, the phenomena with the regular period involve atoms that make transitions between two energy levels at angular frequency ωo. In most atomic clocks realized up to now using alkali metal atoms, these energy levels are part of the ground state of the atoms. The angular frequency ωo involved in these transitions is called the resonance angular frequency and is in the microwave range (Gigahertz range). The transitions can be detected by several means and among others through emission or absorption of energy at the resonance frequency, or when excited at that resonance frequency, by means of effects on a light beam interacting with the same atoms.
The kind of atomic clocks, or more formally, frequency standards, which are of interest in the present context are frequency standards based on the phenomenon of coherent population trapping (CPT). In coherent population trapping, the atoms are subjected to optical radiation at two angular frequencies ω1 and ω2 connecting the two levels of the ground state to a third level called the excited state. When the difference frequency (ω1−ω2) is exactly equal to the atoms' resonance frequency ωo in the ground state, the atoms cannot absorb the electromagnetic radiation or in other words be excited to the excited state. As a consequence, there is no diminution in the optical radiation as it passes through the trapped atoms; also, because none of the trapped atoms can enter the excited state, there is no emission of electromagnetic radiation from the atoms and consequently no fluorescence. When the frequency difference (ω1−ω2) of the optical radiation fields is not exactly equal to the ground state resonance frequency ωo, the atoms are not trapped in the ground state. They can absorb energy from the optical radiation fields, enter the excited state and emit fluorescence. The resonance phenomenon in the ground state at frequency ωo is thus observed directly on the transmitted radiation or fluorescence as a change in intensity. In practice fluorescence is undesirable since it causes incoherent optical pumping. For this reason, nitrogen, which causes decay of the atoms from the excited state without fluorescence, or in other words causes quenching of fluorescence, is used as a buffer gas as will be described below. Thus in practice the CPT effect is detected in transmission.
FIG. 1 is a block diagram of a CPT frequency standard 101 of the type disclosed in U.S. Pat. No. 6,320,427, cited in the Cross references to related applications. At the highest level, frequency standard 101 works as follows: The current source 125 driving laser 103 is modulated by microwave generator 127 at frequency ωo/2. This has the effect of creating, in the output spectrum of the laser, sidebands spaced symmetrically on each side of the laser carrier frequency. These sidebands are separated by ωo/2 and their amplitude is given by Bessel functions Jn. The two first sidebands called J1+ and J1− situated on each side of the carrier are thus separated by the frequency ωo. They are the sidebands used as the two radiation fields at ω1 and ω2. Under the excitation of these two sidebands, the atoms are trapped in the ground state, they cannot absorb the light from the laser and virtually all of the light passes through resonance cell 111 to photodetector 113; when (ω1−ω2) is not equal to ωo the atoms are not trapped in the ground state, much more of the light is absorbed by the atoms in resonance cell 111 and much less light reaches photodetector 113. Photodetector 113 produces a current which is proportional to the amount of light that falls on it, and the current from photodetector 113 thus indicates when (ω1−ω2) is equal to ωo or not.
Microwave generator 127 is modulated at a low frequency causing the frequency separation (ω1−ω2) to vary periodically by a small amount and causing at the same time a low frequency periodic variation of the optical radiation at photodetector 113. This periodic variation is processed as indicated below to lock the microwave generator to the atomic resonance at ωo.
In more detail, resonance cell 111 contains an alkali-metal vapor which is buffered by chemically inert gases to avoid Doppler effect and relaxation of the atoms on the cell walls, which broadens the resonance line as well as to quench the fluorescence. Nitrogen is a preferred buffer gas for this effect. In a preferred embodiment, the alkali vapor is rubidium 87 (87Rb). Before the laser light 105 enters resonance cell 111, it is attenuated by attenuator 107 and circularly polarized by quarter-wave plate 109. The frequency of the sidebands of the frequency-modulated light output from laser 103 is controlled by feedback signal 117 from photodetector output signal 115. This is done by modulating by a small amount the frequency of the microwave generator and using digital synchronous detection techniques. Feedback signal 117 is digitized by A/D converter 119 to produce signal 120. Signal 120 is received by control processor 121, which uses the feedback to derive control signals 123 for microwave generator 127, which generates the microwave frequency by which the frequency of laser 103 is modulated. The microwave frequency is applied to laser current source 125, which provides current to laser 103. In this implementation the microwave generator is locked in frequency to the atomic resonance ωo as determined from photodetector output signal 115. The frequency standard produced by clock 101 is derived from the locked frequency of the microwave generator.
As indicated above, the CPT phenomenon depends on the proper high frequency modulation of the frequency of laser 103. The modulation required is in turn determined by the energy level structure of the alkali metal atoms. The energy level structure of 87Rb is shown at 129. The ground state is S state 131; the excited state is P state 133. The hyperfine levels F=1 and F=2 of ground state 131 are shown at 145 and 147; the hyperfine levels F′=1 and F′=2 of the excited state are shown at 149 and 151.
In the case of hyperfine levels 145 and 147, the difference in energy corresponds to a frequency of 6.835 GHz, as shown at 153. This is the atom ground state resonance frequency, ωo/2π, used in the implementation of the CPT Rb87 frequency standard. Other alkali metal atoms have different resonance frequencies and can also be used. Referring to FIG. 1, the preferred frequencies in the present embodiment are those corresponding to the transitions 137 (ω1) and 141 (ω2). If the difference frequency (ω1−ω2) is equal to ωo, the atoms in ground state 131 are trapped in that state and cannot make a transition to excited state 133. As indicated above, the transitions are caused by photons from laser 103, and when a photon causes a transition, it is absorbed by resonance cell 111 and does not reach photodetector 113. When the atoms cannot make the transitions, resonance cell 111 absorbs very little of laser light 105 and almost all of it reaches photodetector 113. In system 101, the two frequencies necessary to produce CPT are produced by modulating the current source of laser 103 at a microwave frequency which is ½ of frequency 153. Another technique consists in using an electrooptic modulator (EOM) placed directly in the light beam 105 and driven by a microwave generator similar to 127.
In such cases the spectrum of the modulated laser contains sidebands whose amplitudes are determined by Bessel functions as explained above. The two first sidebands J1 are those used in the detection of the CPT phenomenon and the size of the detected resonance signal is a function of their amplitude. On the other hand, the so-called light shift, affecting the resonance frequency ωo and the precision of the frequency standard, is a function of the amplitude of all the sidebands contained in the laser spectrum. These amplitudes depend on the microwave power applied on the current source driving the laser. The amplitude of all these sidebands is characterized by the so-called modulation index m which is a measure of the depth of modulation. For example for maximum J1's the modulation index must be set at m=1.8, while for minimum light shift the modulation index must be set at m=2.4. It is thus important to have control on this modulation index depending on the condition desired.
A problem in making frequency standards 101 has been that the standard technique for determining the modulation index of light 105 produced by a laser has been the need to remove the laser from the frequency standard and/or use a specialized optical spectrum analyzer to determine the laser's modulation index. Under even the best of circumstances, this procedure is time consuming and fraught with all of the risks involved in removing and reinstalling a component of a precision device. However, one of the great advantages of frequency standards like frequency standard 101 is their small size; current versions in which the whole device is 7 cm. long have been produced and versions which are 4.2 mm long and 1.5 mm square, and thus small enough to be a component of an integrated circuit, are under discussion. As the frequency standards become smaller, it becomes ever more difficult and finally impossible to remove the laser to determine its modulation index. What is needed, and what is provided by the present invention, is a technique for determining the modulation index of the laser without removing the laser from the frequency standard. It is thus an object of the invention to provide such a technique.